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Proof step 1 from proof key-size (conclusion)

∀ a. a ∈ st ↔ a ∈ st0 ⊦ # st = # st0

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ a. a ∈ ∅ ↔ a ∈ st0 ⊦ # ∅ = # st0
Proof step 6:
∀ st0. (∀ a. a ∈ st1 ↔ a ∈ st0) → # st1 = # st0, ∀ a0. a0 ∈ st1[a, d] ↔ a0 ∈ st0 ⊦ # st1[a, d] = # st0

Rule argument

indvar: st

Additional information

Used simplifier rules: gen-04: ⊦ ;